R.Marshall
I think you can forget about the 260 or anything on the 308 case, they are too short. I'm leaning now toward 6.5x55 as suggested by SKB. I wouldn't think a 6.5x57 cartridge would chamber in a 6.5x55, but maybe there are enough tolerance differences in the right places to allow it. I note the 12.18 mm measurement you got from the fired case is about the same as the head diameter listed for the 6.5x55. My brother had a 6.5x55 rifle and used American cases in it( I think Rem., but maybe Win.). These cases did not have the larger head diameter, rather, they had the same size as 30-06/308/270. If you try an American 6.5x55 cartridge then, it will likely expand a lot also. It is hard to tell from the photo of the fired case, but it seems it has shortened some. This is common when a case expands a good bit ( the brass has to come from somewhere). Also I still believe the 6.5x58 P. has too much taper in the case and neck to be the correct cartridge. I went back to the earlier posts and the rifle does have the early type firing pin, I believe. Can you post a photo of the tip of the firing pin? You still have the problem of light firing pin strikes we have to work out(it would still be good to measure the firing pin protrusion).
Mike